Chapter 14, Problem 74GQ

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

The gas-phase reaction2 N2O5(g) → 4 NO2(g) + O2(g)has an activation energy of 103 kJ/mol, and the rate constant is 0.0900 min−1at 328.0 K. Find the rate constant at 318.0 K.

Interpretation Introduction

Interpretation:

For the given reaction under given conditions, the rate constants for temperature 318.0K should be determined.

Concept introduction:

In order to establish the plausibility of a mechanism, one must compare the rate law of the rate determining step to the experimentally determined rate law.

Rate determining step: In a chemical reaction the rate determining step is the slowest step in which the rate of the reaction depends on the rate of that slowest step.

Rate law: It is generally the rate equation that consists of the reaction rate with the concentration or the pressures of the reactants and constant parameters.

Rate constant: The rate constant for a chemical reaction is the proportionality term in the chemical reaction rate law which gives the relationship between the rate and the concentration of the reactant present in the chemical reaction.

Rate order: The order of each reactant in a reaction is represented by the exponential term of the respective reactant present in the rate law and the overall order of the reaction is the sum of all the exponents of all reactants present in the chemical reaction.  The order of the reaction is directly proportional to the concentration of the reactants.

Activation energy: It is defined as the minimum energy required by the reacting species in order to undergo chemical reaction.

Intermediate species: It is the species formed during the middle of the chemical reaction between the reactant and the desired product.

Arrhenius equation:

• Arrhenius equation is a formula that represents the temperature dependence of reaction rates
• The Arrhenius equation has to be represented as follows

k=AeEa/RTlnk=lnAeEa/RTlnk=(EaR)(1T)+lnA

• Ea represents the activation energy and it’s unit is kJ/mol
• R represents the universal gas constant and it has the value of 8.314 J/K.mol
• T represents the absolute temperature
• A represents the frequency factor or collision frequency
• e represents the base of natural logarithm
•  Arrhenius equation equation was proposed by Svante Arrhenius in 1889.
Explanation

Given:

â€‚Â T1=318Kâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€ŠK1â€Šâ€Š=â€Šâ€Š?T2â€Šâ€Šâ€Š=â€Šâ€Š328Kâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€ŠK2=â€Šâ€Š0.0900minâˆ’1Ea=103kJ/mol

In order to find the rate constant at given temperature we need to use the following Arrhenius rate expression which relates the rate constant, activation energy and the temperature.

â€‚Â log(K2K1)â€Šâ€Š=â€Šâ€ŠEa2.303R(1T1-1T2)

With known rate constant, temperature and the activation energy the rate constant for the other given temperature is calculated as follows,

Â â€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šlog(0.0900minâˆ’1K1)â€Šâ€Š=â€Šâ€Š103Ã—103J/mol2

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